Question

1. Given a ⎜⎜ b, m∠1 = 56°, and m∠2 = 42°, find the measure of the other angles.
   Note: Angles may not be drawn to scale.

10 9 6 1 4 3 14 X12 13

Answer 1

Explanation:

1. Angle 1 = Angle 4 = 56 ( Vertically Opposite Angles)

2. Angle 2 = Angle 5 = 42  ( Vertically Opposite Angles)

3. Angle 3 = 180 - ( Angle 1 + Angle 2) (Linear Pair)

= 180 - (56 + 42) = 82

4. Angle 3 = Angle 6 = 82 ( Vertically Opposite Angles)

5. Angle 6 = Angle 8 = 82 ( Alternate Angles)

6. Angle 7 = 180 - Angle 8= 180 - 82 = 98 (Linear Pair)

7. Angle 8 = Angle 10 = 82  ( Vertically Opposite Angles)

8. Angle 7 = Angle 9 = 98 ( Vertically Opposite Angles)

9. Angle 4= Angle 11= 56 (Alternate angles)

10. Angle 11= Angle 13 = 56 ( Vertically Opposite Angles)

11. Angle 12= 180 - (Angle 11) ( Linear Pair)

= 180 - 56= 124

12. Angle 12 = Angle 14 = 124 ( Vertically Opposite Angles)

Final Answers:

Angle 3 = 82

Angle 4 = 56

Angle 5 = 42

Angle 6 = 82

Angle 7 = 98

Angle 8 = 82

Angle 9 = 98

Angle 10 = 82

Angle 11= 56

Angle 12= 124

Angle 13 = 56

Angle 14 = 124